Suspect team member is undiagnosed ND

What is your workplace's disability policy OP?
At mine, you don't need a diagnosis to request reasonable adjustments. You do need an occupational health assessment.

Also, currently you're all supportive, but no job lasts forever. What happens if your colleague gets a new one? In another workplace whether they struggle?

If you've been 'covering' for your colleague up to this point, it's in their long-term interests to have their shortcomings point out. You can then mention that it looks like ND traits.

At least they can start the process or go private if they want to.

BTW I have suspected ND and even before seeking a formal diagnosis I found online resources etc extremely helpful. So just raising the possibility isn't worthles

Whatever the 'something' that has come up is, if it could be of benefit to anyone on the team with a neurodiversity then the best approach is probably to let the whole team know that it exists and how to access it.

Getting an NHS assessment is almost impossible as an adult, so unless your colleague can pay privately, the absolute best case scenario is that they would be stuck on a very long waiting list (but many GPs won't even refer).

Unless your colleague opens up to you and asks for advice/support, I don't think you can bring this up - it might be very shocking to them if it's something they have never considered.

If the 'something' that has come up is, e.g. an event for neurodivergent colleagues your best approach would be to promote this across the whole team rather than singling one person out.

NHS queues for ND assessments are years long even assuming the waiting lists are open at all.

Many GPs will not refer unless there is significant evidence of problems in daily life (and they are likely to feel that holding down a job means no problems)

You could mention it but unless they have a lot of spare cash or know someone who does it won't change anything.

I guess you could offer the course with a caveat that team member may find it helpful despite not being diagnosed with ND, and suggest they enquire ‘in case there is additional capacity’.

I’m guessing this is an opportunity specifically aimed at people with NDs so OP can’t recommend it to the team member without implying they have ND. Otherwise, you’d just suggest/offer without a second thought, I’d imagine.

It’s not your place to say anything. You don’t even know if they think they may be ND but don’t want a formal diagnosis (or interfering work colleagues trying to organise their work lives).
If support is needed then facilitate that support if that’s part of your role at work. Otherwise, keep out of it.

The diagnosis is irrelevant. If they need support, you give them support. Reasonable adjustments are based on challenges and needs in the workplace, not on diagnosis. The Equality Act is quite clear on that and, if HR is pushing for the diagnosis before agreeing to OH assessment, they should be encouraged to read it.
ETA: this does not even account for the fact that ND assessment can take years to come through and all this time the person is not getting any workplace support if their eligibility is diagnosis-based.